Tunneling in Graphene-Topological Insulator Hybrid Devices
Hybrid graphene-topological insulator (TI) devices were fabricated using a mechanical transfer method and studied via electronic transport. Devices consisting of bilayer graphene (BLG) under the TI BiSe exhibit differential conductance characteristics which appear to be dominated by tunneling, roughly reproducing the BiSe density of states. Similar results were obtained for BLG on top of BiSe, with 10-fold greater conductance consistent with a larger contact area due to better surface conformity. The devices further show evidence of inelastic phonon-assisted tunneling processes involving both BiSe and graphene phonons. These processes favor phonons which compensate for momentum mismatch between the TI and graphene points. Finally, the utility of these tunnel junctions is demonstrated on a density-tunable BLG device, where the charge-neutrality point is traced along the energy-density trajectory. This trajectory is used as a measure of the ground-state density of states.
pacs:73.40.Gk, 73.50.-h, 73.20.At
March 21, 2018
In topological insulators (TIs), the protected surface state is bound to the interface between materials with different bulk topological invariants (1). Although the surface state will remain gapless as long as the symmetries protecting the bulk topological invariant are retained, its dispersion and location depend on the band-structures of the two interfacing materials. A model system allowing the investigation of such interface properties is the graphene-TI hybrid, where graphene resides in immediate proximity to the TI, separating it from the vacuum or from another trivial dielectric. Indeed, as part of a 3D continuum, graphene is topologically trivial. However, with a significant spin-orbit (SO) term, graphene could become a 2D TI (2).
Recent studies (3); (4); (5); (6) which theoretically investigate the properties of such hybrids, generally assume that the graphene and TI bands couple strongly, leading to fundamental modifications to the graphene band structure, which is expected to inherit an enhanced SO coupling (3) and attain non-trivial spin-textures (6). When sandwiched between two ultra thin layers of BiSe, the graphene layer may become a 2D TI (5). However, as the surface states of TIs such as BiSe are centered at the point in -space, they should be prevented by momentum conservation from hybridizing with the graphene bands, centered at the points. This difficulty is often resolved theoretically by assuming that periodicity at the interface would cause the graphene Brillouine zone (BZ) to fold (3); (4); (5); (6), bringing significant spectral weight to the point.
Here we present an experimental study of graphene-TI hybrid devices fabricated using a mechanical transfer technique (7) which allows the fabrication of vertical heterostructures involving a wide variety of van-der-Waals materials. In our devices, which consist of either monolayer (MLG) or bilayer graphene (BLG) stacked above or below the TI BiSe, the graphene and TI layers are weakly coupled, with transport between them governed by tunneling. The devices reveal a rich inelastic spectrum consisting of graphene and BiSe phonons. Finally, we demonstrate the utility of the interface tunnel-junction to probe the density-dependent evolution of spectral features in BLG.
Fig. 1(a) shows Device 1, where a BiSe flake is transferred on top of a BLG flake (outlined in green) deposited on SiO. The flakes are independently contacted by evaporated metallic electrodes (Fig. 1(b)). The BLG-TI junctions are studied by measuring the differential conductance vs. applied bias voltage with the source on one material and the drain on the other (TI1 to G1). A four-probe geometry is realized by measuring the voltage across the opposing contacts ( = V(TI2)-V(G2)). The trace at of Device 1 (Fig. 1(c)) shows a pronounced suppression at negative values, similar to STM measurements taken on BiSe (8); (9); (10), where is proportional to the density of states (DOS) and the suppression at negative bias is associated with the bulk gap of the BiSe. The BLG-TI interface therefore behaves as an effective tunnel junction although no intentional barrier was placed between the materials. It is a remarkably robust junction, maintaining a stable signal while sustaining high voltage biases exceeding 0.5 V at negative bias.
The tunneling functionality of the graphene-BiSe interface could be a consequence of BiSe oxidation (11). In over 20 devices studied, the interface resistance varied from 10 M to 10 , which could be associated with varying degrees of oxidation. The stability and high bias achieved by graphene-TI junctions, however, do not favor this explanation – oxide-based junctions rarely function at biases in excess of 200 meV (12). Alternatively, the variation in interface resistance could arise due to differences in the effective contact area: graphene conforms to the underlying substrate and has angstrom-scale height variations when deposited on SiO resulting in an effective partial contact area. To test this we studied devices where BLG is deposited on top of BiSe: in Device 2 a single BLG flake covers two BiSe flakes (Fig. 1(d-e)). Measured separately (red and blue curves in panel (f)), the two junctions exhibit comparable characteristics which are very similar to the “graphene on bottom” devices (albeit with smaller bias range).
The interface conductivity of “graphene-on-top” junctions is an order of magnitude greater than “graphene on bottom” ones, indicating that the effective contact area is a plausible source of variation. It is not clear, however, what is the origin of the generic tunneling functionality. An interesting possibility is that the tunnel barrier is associated with the lack of direct chemical bonding between the two layers. Inter-layer tunnel barriers in layered materials is observed in high Tc superconductors (13) and in vdW materials such as 4Hb- (14). Incoherent interlayer transport was also reported in stacked twisted bilayer graphene devices (15), and graphene layers could be weakly coupled to underlying graphite (16). Testing this hypothesis would require further investigation.
As expected, the characteristics vary with the choice of MLG vs. BLG. The tunneling current is expressed as a convolution of the graphene DOS and the TI DOS (17)
where is the effective overlap area and stands for the tunnel coupling through the barrier. This expression is qualitatively depicted in the schematics in Fig. 1(g,h), showing on the left and (including bulk and surface) on the right. For BLG devices (panel (g)) is relatively featureless and can be factored out of the integral, so the curve effectively probes . This explains why BLG-TI traces are similar to STM measurements of BiSe, and suggests that BLG may be useful as a tunneling electrode for probing other vdW systems. MLG-TI devices (panel (h)) have energy-dependent on both sides of the barrier, and Device 3 (Fig 2(a)) indeed exhibits a very different characteristic, with a stronger suppression around zero-bias which we associate with the graphene Dirac point.
Tunnel junctions are useful in measuring inelastic spectra, where the onset of processes such as phonon-assisted tunneling appears as step-increase features in the differential conductance. These are detectable as peaks in the 2nd derivative at bias voltages corresponding to the phonon energies. It is possible to differentiate between BiSe and graphene phonons because their respective spectra span different energy ranges (up to 20 meV for BiSe (19), and up to 200 meV for graphene (20)). Several devices exhibit well-developed inelastic spectra: Device 3 (Fig. 2(a)), has sharp step-like features in close to zero (inset). The corresponding plot (Fig. 2(b)), shows peaks at 7.7 meV which coincide in Device 3 (MLG) and in Device 1 (BLG). We associate this feature with a BiSe surface optical phonon previously identified using Helium scattering at the same energy (21). This phonon plays a role in suppressing surface transport (22), and inelastic tunneling data may be useful in probing its coupling to surface electrons.
Signatures of graphene phonons, appearing at higher bias voltages, are found in numerous devices. For example, in Device 4 (Fig. 2(c,d)), a higher quality device fabricated by deposition of BLG on h-BN followed by transferring BiSe on top. The plot shows a prominent peak at 67 meV, corresponding to the energy of the graphene ZA/ZO mode at the points. This phonon is seen in many graphene and graphite tunneling experiments both in devices (23) and in STM (24); (25), and is generally believed to assist the tunneling process by providing the momentum required to inject an electron to the points. In our devices, where graphene and BiSe Fermi surface momenta are highly mismatched, it is likely that the same phonon is required to allow momentum-conserving tunneling from low energy BiSe states, centered at the point, to the graphene points (Schematic in inset to Fig. 2(d)). Device 4 also exhibits a feature at 162 meV associated with the LA/LO mode, also a phonon, and a feature at 195 meV associated with the TO mode at . Other features (e.g. a phonon at 36 meV) could be associated with the h-BN substrate (23).
In the rest of this Letter we focus on Device 5, which has the same geometry as Device 1: TI on top of a density-tunable BLG flake. Device 5 can be measured by graphene in-plane transport (G1 to G2) or by tunneling (T1 to G1). In-plane resistance is presented in Fig. 3(c), showing a resistance peak when the chemical potential crosses the BLG CNP. The BiSe electrode acts as a well-behaved gate, and the small tunneling current does not interfere with the in-plane measurement. The resistance map is typical of doubly-gated graphene (26); (27), where the diagonal feature corresponds to a high resistance state in the BLG region underneath the TI. This feature intercepts at , indicating that the BLG is p-doped and the CNP is energetically mismatched from the TI DP (Fig. 3(a) annotation I). Its slope is dictated by the requirement that the top and bottom gates compensate each other’s charge (annotation II) and therefore follows the ratio ( and are the graphene-TI and graphene-back gate capacitances, respectively). Using this relation, we extract the geometric capacitance of the TI-BLG junction , 110 times greater than the back-gate capacitance. Both the relative permittivity of the interlayer medium, , and the graphene-BiSe effective distance, , are unknown. However, the measured value of fixes their ratio to nm. As the interface is a tunnel junction, is unlikely to exceed nm, setting a limit of .
Gate-dependent tunneling measurements are presented in Fig. 3(d-e): Such measurements are sensitive to energy shifts in the spectral features due to the changes in density. In Fig. 3(d) it is clear that the underlying structure of the BiSe gap at negative is retained while a set of features closer to zero bias evolve with . To trace these features we plot the second derivative as a color map in Fig 3(e). The data exhibit a set of diagonal features with opposite slopes and gate-independent features which appear as faint vertical lines. The latter gate-independent features are enhanced by averaging over all back-gate values (Fig. 3(b)), where we again find the ZA/ZO phonon features at 65 meV. The 22 meV feature coincides with the energy of the BiSe phonon (19).
changes the graphene density, vertically shifting the band-structure (Fig. 3(a), annotation III). To trace a spectral feature such as the CNP, a voltage has to be applied to compensate for the density-induced change in chemical potential, . This is formulated as:
To trace spectral features on the - plane, we have to note that planar tunneling electrodes are large capacitors which charge the graphene layer at finite bias, as discussed earlier. The equations governing the charging of the graphene layer connect the incremental gate voltages to the incremental charges on the back-gate and TI :
Interestingly the CNP tunneling condition in Eq. 2 also ensures that there will be no extra charge accumulated on the TI (), as the argument in parenthesis in Eq. 3 remains zero. More generally, this means that constant energy features lie on trajectories which keep the charge on the tunneling electrode fixed. In the Supplementary Information (18) we derive the CNP-tunneling trajectory and find its slope to be:
where is the quantum capacitance of the BLG. The slope is independent of , consistent with the induced charge on the TI remaining zero.
As a result, Eq. 4 can be used to evaluate by fitting the slope of the features appearing in the figure. The most prominent feature in Fig. 3(e), marked by “III”, is likely the charge neutrality point, which attains a cusp in the DOS due to a finite displacement field (annotation I). The slope of this feature is not constant, and appears to vary along the trajectory (Fig. S1). This indicates that , and hence the DOS, changes with density, as expected for the hyperbolic dispersion of BLG (28); (29); (30).
We fit the expected trajectory (Fig. 3(e), feature “III”). To calculate this fit it is crucial to acknowledge that the BLG dispersion varies within the plane, where at each point the displacement field is different. The calculation, described in the SI (18), is carried out self-consistently, using an approximate trajectory for calculating the displacement field at each value of and . We then extract , and finally and integrate the trajectory from the slope in Eq. 4. The calculation is refined iteratively. Using the Fermi velocity as a fitting parameter, the full trajectory can be reproduced with , in good agreement with non-interacting values for BLG.
Multiple replica (marked by IV in Fig. 3(e)) of the CNP tunneling feature, appear as lines running parallel to the elastic feature (“IV”). They are associated with phonon-assisted inelastic tunneling processes to the CNP. Unlike the gate-independent phonon-onset features discussed above, where tunneling takes place to the Fermi energy, these features represent phonon-assisted tunneling to some sharp spectral feature (here the CNP), and evolve with the gate in parallel to the elastic tunneling feature. Their trajectories, presented in Fig. S1, should depend on the elastic feature, after accounting for modified displacement fields at higher bias. However, to fit the actual data we find that the Fermi velocities have to be modified in each of the inelastic features (assuming interlayer coupling remains fixed). The modified Fermi velocities are m/s for the -22 mV feature, and m/s for the -65 mV feature. This points, perhaps, to velocity renormalization.
In summary, the graphene-BiSe interface is a high quality tunnel junction which can be integrated in to a density-tunable device. Further studies are required to address the effect of junction properties such as crystallographic orientation, interface quality and the effect of BiSe oxidation. Phonon-assisted tunneling is observed at finite bias, with specific phonon-activation processes which bridge the mismatch in crystal-momentum between the two materials. Nevertheless, tunneling in general is not momentum conserving, probably due to junction inhomogeneity or other scattering processes. The role of the surface state in the tunneling process is also an open question: where some device (Device 1) seem to reveal evidence of bulk states in the tunneling signal, others (Device 4) appear to be mostly surface-dominated.
This work was supported by the DOE, Basic Energy Sciences Office, Division of Materials Sciences and Engineering, under Award No. DE-SC0006418. This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities supported by NSF under Grant No. DMR-0819762. Sample fabrication was performed partly at the Harvard Center for Nanoscale Science supported by the NSF under Grant No. ECS-0335765.
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